This invention relates to coherent pulse-doppler tracking radar, and more particularly to a system for resolving the ambiguity in target velocity estimates made from doppler shift measurements.
The concept of pulse transmission has been basic to most tracking radar systems because range can be easily measured by the time delay of each pulse round trip. Information as to the relative radial velocity of the target is determined by measuring the doppler frequency shift between transmitted and reflected waves of each pulse, and information as to the angular coordinates of the target is determined by relating received energy properties to the sensitivity and directivity patterns of the antenna.
A relative high pulse repetition frequency (PRF) is commonly employed to provide unambiguous velocity (doppler shift) determination, but range is then usually ambiguous. To resolve the range ambiguity, it is common practice to use a staggered PRF, i.e., to alternate the period of the radar pulse cycle. Both range and doppler shift can then be tracked without ambiguity. However, it is often desirable to use a medium PRF, namely a PRF that is not sufficiently high in relation to the largest expected values of doppler-shift for velocity to be tracked unambiguously. If doppler shift cannot be unambiguously tracked, the target's velocity relative to the velocity of the aircraft carrying the radar system cannot be determined except by the range tracking loop, i.e., by effectively taking the first derivative of range measurements. Doppler-shift measurements provide more accurate determination of velocity. Moreover, the determination can be made on the basis of the most recent radar return alone. The problem is to provide a radar tracking system with the facility for resolving the ambiguity in velocity.
A typical tracking system in a tactical aircraft performs two principle functions. First, it positions the antenna and the range and velocity gates of the radar signal processor, so as to keep the target accurately centered within the "field of view" of those elements. Second, it generates estimates of the target's position and motion for use in fire-control and aircraft-steering computations. These functions must be accurately performed over an extremely broad range of operating conditions, ranging from highly dynamic dog-fight encounters at short-range to very low signal-to-noise ratios at long range.
Several factors must be dealt with in the design of the tracking system in order to obtain the required accuracies and performance capabilities. First, there is the problem of measurement errors due to factors such as noise, target scintillation, and radome refraction. Maneuvers of the target and deception techniques (countermeasures) employed by targets to prevent tracking are the second class of problems which must be dealt with.
Due to the large variations in the characteristics and magnitudes of these error sources over the wide spectrum of operating conditions, variable parameter filters are necessary to meet tracking accuracy requirements of high performance aircraft. For example, narrow bandwidth filtering is required for tracking targets at long range with low signal-to-noise ratios. But rapid response is necessary for tracking highly maneuverable targets at short range. These factors, plus the requirement for generating high accuracy estimates of target line-of-sight (LOS) rates, and the desirability of employing one unified set of general filter equations to handle any radar mode --high PRF, medium PRF, low PRF, and so forth-- have led to the use of a new approach in the design of the tracking filter using Kalman filtering.
A system employing this new approach is like a typical radar tracking system in that a target reflects pulses to an antenna which analyses the return pulses and provides the desired information. A transmitter and receiver is operated in accordance with a predetermined mode in regard to frequency and PRF, both of which are often selected automatically or by an operator for a particular target to avoid velocity and range blind zones. The receiver provides video signals to a radar signal processor which produces signals that are measurements of range, range rate (radial velocity) and angular coordinates (elevation and azimuth deflection) of the target. These measurement signals are then applied to standard antenna controllers for positioning the antenna and to range and velocity controllers for positioning range and velocity gates. A typical radar tracking is thus a multiple closed-loop feedback system. Two loops for tracking in azimuth and elevation, and two loops for tracking in range and velocity. Standard servomechanism design procedures are both applicable and practical to each of these loops, but optimal results are not always achieved by such procedures.
The difference between this new approach and the prior art is that the prior art tracking loops have employed classical single control loops, using low-pass filtering to remove noise from measurement signals, whereas the new approach employs more advanced control loops employing filters for estimating quantities from measured differences between estimates and actual measurements, such as .DELTA.R.sub.m = R - R.sub.m. The timing of a range gate, R.sub.G, represents the range estimate, R, and the time of arrival of a round-trip radar pulse represents the measured range, R.sub.m. The difference then is the discriminant, .DELTA.R.sub.m. The range servo-loop continually updates the range estimate R to drive .DELTA.R.sub.m toward zero. Analogous servomechanism procedures drive the velocity discriminant, V.sub.m, toward zero and the azimuth and elevation discriminants, .DELTA..eta..sub.m and .DELTA..epsilon..sub.m, toward zero.
In accordance with this new approach, an airborne system is provided with electromagnetic energy sensors for tracking moving targets is some or all of range, radial velocity, elevation and azimuth. Energy received from the system sensors is processed to develop signals representing actual discriminants of range, .DELTA.R.sub.m, radial velocity, .DELTA.V.sub.m, elevation, .DELTA..epsilon..sub.m, and azimuth, .DELTA..eta..sub.m. These measurements are used to generate predictions of the next measurements from current estimates of system states, where the states are vectors X.sub.R (i), X.sub.V (i), X.sub.e (i) and X.sub.d (i), using for each state an equation of the general form EQU X.sub.i.sub.+l = .phi..sub.i X.sub.i + L.sub.i + K.sub.i (Y.sub.i - H.sub.i X.sub.i) (1)
where X is a state vector, .phi. is a transition matrix, L is a vector of dynamical aiding terms to compensate for rotational rates and inertial acceleration of the antenna, K is a gain factor, Y is the output of a measurement structure for the dynamical system and H is a system scaling factor which accounts for the gain in the measurement structure. The four channels implemented in accordance with this general equation are cross-coupled by using outputs of one or more channels as parameters in the remaining channels. For the range channel
R.sub.TPR X.sub.R = V.sub.TPR a.sub.TPR
thus generating estimates of predicted target range, R.sub.TPR, radial velocity, V.sub.TPR, and radial acceleration, a.sub.TPR. For the velocity (doppler) channel
V.sub.TPV X.sub.V = a.sub.TPV
thus generating estimates of predicted doppler velocity V.sub.TPV and acceleration a.sub.TPV. For the antenna angle channels
.epsilon..sub.Pe .epsilon..sub.Pd .omega..sub.LSPe .omega..sub.LSPd X.sub.e = a.sub.Td X.sub.d = a.sub.Te S.sub.e S.sub.d
thus generating estimates of pointing errors, .epsilon..sub.e,d, target line-of-sight rates, .omega..sub.LSPe,d, target accelerations normal to the line of sight, a.sub.Td,e, and target angular scintillation, S.sub.e,d, all referenced directly to antenna coordinates. The pointing error estimates, .epsilon..sub.Pe and .epsilon..sub.Pd, and the target line-of-sight rates .omega..sub.LSPe and .omega..sub.LSPd are used to produce antenna elevation and azimuth commands .omega..sub.Ce and .omega..sub.Cd. The range estimate R.sub.TPR and the velocity estimate V.sub.TPV are used to produce a range gate command, R.sub.GC, and a velocity gate command, V.sub.GC, both to be used by a radar controller.
In operation of the tracking system, measurements of SNR are made coincidentally with the discriminant measurements. The discriminant noise variance and the discriminant slope are then determined from the measured SNR, and these quantities are utilized in the calculations of the filter gains. Thus, the filter is provided with data on discriminant used by the filter, thereby adapting the filter to the characteristics of each measurement sample.